9 Answers
9

Preliminaries

On modern computers, only the lowest level memory structures (the registers) can move data around in single clock cycles. However, registers are very expensive and most computer cores have less than a few dozen registers (few hundred to maybe a thousand bytes total). At the other end of the memory spectrum (DRAM), the memory is very cheap (i.e. literally millions of times cheaper) but takes hundreds of cycles after a request to receive the data. To bridge this gap between super fast and expensive and super slow and cheap are the cache memories, named L1, L2, L3 in decreasing speed and cost. The idea is that most of the executing code will be hitting a small set of variables often, and the rest (a much larger set of variables) infrequently. If the processor can't find the data in L1 cache, then it looks in L2 cache. If not there, then L3 cache, and if not there, main memory. Each of these "misses" is expensive in time.

(The analogy is cache memory is to system memory, as system memory is to hard disk storage. Hard disk storage is super cheap, but very slow).

Caching is one of the main methods to reduce the impact of latency. To paraphrase Herb Sutter (cfr. links below): increasing bandwidth is easy, but we can't buy our way out of latency.

Data is always retrieved through the memory hierarchy (smallest == fastest to slowest). A cache hit/miss usually refers to a hit/miss in the highest level of cache in the CPU -- by highest level I mean the largest == slowest. The cache hit rate is crucial for performance, since every cache miss results in fetching data from RAM (or worse ...) which takes a lot of time (hundreds of cycles for RAM, tens of millions of cycles for HDD). In comparison, reading data from the (highest level) cache typically takes only a handful of cycles.

In modern computer architectures, the performance bottleneck is leaving the CPU die (e.g. accessing RAM or higher). This will only get worse over time. The increase in processor frequency is currently no longer relevant to increase performance. The problem is memory access. Hardware design efforts in CPUs therefore currently focus heavily on optimizing caches, prefetching, pipelines and concurrency. For instance, modern CPUs spend around 85% of die on caches and up to 99% for storing/moving data!

There is quite a lot to be said on the subject. Here are a few great references about caches, memory hierarchies and proper programming:

Agner Fog's page. In his excellent documents, you can find detailed examples covering languages ranging from assembly to C++.

Main concepts for cache-friendly code

A very important aspect of cache-friendly code is all about the principle of locality, the goal of which is to place related data close in memory to allow efficient caching. In terms of the CPU cache, it's important to be aware of cache lines to understand how this works: How do cache lines work?

The following particular aspects are of high importance to optimize caching:

Temporal locality: when a given memory location was accessed, it is likely that the same location is accessed again in the near future. Ideally, this information will still be cached at that point.

Spatial locality: this refers to placing related data close to eachother. Caching happens on many levels, not just in the CPU. For example, when you read from RAM, typically a larger chunk of memory is fetched than what was specifically asked for because very often the program will require that data soon. HDD caches follow the same line of thought. Specifically for CPU caches, the notion of cache lines is important.

A simple example of cache-friendly versus cache-unfriendly is c++'s std::vector versus std::list. Elements of a std::vector are stored in contiguous memory, and as such accessing them is much more cache-friendly than accessing elements in a std::list, which stores its content all over the place. This is due to spatial locality.

A very nice illustration of this is given by Bjarne Stroustrup in this youtube clip (thanks to @Mohammad Ali Baydoun for the link!).

Don't neglect the cache in data structure and algorithm design

Whenever possible, try to adapt your data structures and order of computations in a way that allows maximum use of the cache. An common technique in this regard is cache blocking(Archive.org version), which is of extreme importance in high-performance computing (cfr. for example ATLAS).

Know and exploit the implicit structure of data

Another simple example, which many people in the field sometimes forget is column-major (ex. fortran,matlab) vs. row-major ordering (ex. c,c++) for storing two dimensional arrays. For example, consider the following matrix:

1 2
3 4

In row-major ordering, this is stored in memory as 1 2 3 4; in column-major ordering this would be stored as 1 3 2 4. It is easy to see that implementations which do not exploit this ordering will quickly run into (easily avoidable!) cache issues. Unfortunately, I see stuff like this very often in my domain (machine learning). @MatteoItalia showed this example in more detail in his answer.

When fetching a certain element of a matrix from memory, elements near it will be fetched as well and stored in a cache line. If the ordering is exploited, this will result in fewer memory accesses (because the next few values which are needed for subsequent computations are already in a cache line).

For simplicity, assume the cache comprises a single cache line which can contain 2 matrix elements and that when a given element is fetched from memory, the next one is too. Say we want to take the sum over all elements in the example 2x2 matrix above (lets call it M):

In this simple example, exploiting the ordering approximately doubles execution speed (since memory access requires much more cycles than computing the sums). In practice the performance difference can be much larger.

Avoid unpredictable branches

Modern architectures feature pipelines and compilers are becoming very good at reordering code to minimize delays due to memory access. When your critical code contains (unpredictable) branches, it is hard or impossible to prefetch data. This will indirectly lead to more cache misses.

In the context of c++, virtual methods represent a controversial issue with regard to cache misses (a general consensus exists that they should be avoided when possible in terms of performance). Virtual functions can induce cache misses during look up, but this only happens if the specific function is not called often (otherwise it would likely be cached), so this is regarded as a non-issue by some. For reference about this issue, check out: What is the performance cost of having a virtual method in a C++ class?

Common problems

A common problem in modern architectures with multiprocessor caches is called false sharing. This occurs when each individual processor is attempting to use data in another memory region and attempts to store it in the same cache line. This causes the cache line -- which contains data another processor can use -- to be overwritten again and again. Effectively, different threads make each other wait by inducing cache misses in this situation.
See also (thanks to @Matt for the link): How and when to align to cache line size?

An extreme symptom of poor caching in RAM memory (which is probably not what you mean in this context) is so-called thrashing. This occurs when the process continuously generates page faults (e.g. accesses memory which is not in the current page) which require disk access.

perhaps you could expand the answer a bit by also explaining that, in -multithreaded code- data can also be too local (e.g. false sharing)
– TemplateRexMay 22 '13 at 19:41

2

There can be as many levels of cache as the chip designers think is useful. Generally they are balancing speed vs. size. If you could make your L1 cache as big as L5, and just as fast, you would only need L1.
– Rafael BaptistaMay 22 '13 at 20:00

20

I realise empty posts of agreement are disapproved of on StackOverflow but this is honestly the clearest, best, answer I've seen so far. Excellent work, Marc.
– Jack AidleyMay 22 '13 at 21:24

1

@JackAidley thanks for your praise! When I saw the amount of attention this question received, I figured many people may be interested in a somewhat extensive explanation. I'm glad it's useful.
– Marc ClaesenMay 22 '13 at 21:29

1

What you didn't mention is that cache friendly data structures are designed to fit within a cache line and aligned to memory to make optimal use a cache lines. Great answer though! awesome.
– MattMay 22 '13 at 21:32

In addition to @Marc Claesen's answer, I think that an instructive classic example of cache-unfriendly code is code that scans a C bidimensional array (e.g. a bitmap image) column-wise instead of row-wise.

Elements that are adjacent in a row are also adjacent in memory, thus accessing them in sequence means accessing them in ascending memory order; this is cache-friendly, since the cache tends to prefetch contiguous blocks of memory.

Instead, accessing such elements column-wise is cache-unfriendly, since elements on the same column are distant in memory from each other (in particular, their distance is equal to the size of the row), so when you use this access pattern you are jumping around in memory, potentially wasting the effort of the cache of retrieving the elements nearby in memory.

This effect can be quite dramatic (several order of magnitudes in speed) in systems with small caches and/or working with big arrays (e.g. 10+ megapixels 24 bpp images on current machines); for this reason, if you have to do many vertical scans, often it's better to rotate the image of 90 degrees first and perform the various analysis later, limiting the cache-unfriendly code just to the rotation.

Modern image editors use tiles as internal storage, e.g. blocks of 64x64 pixels. This is much more cache-friendly for local operations (placing a dab, running a blur filter) because neighbouring pixels are close in memory in both directions, most of the time.
– maxyMay 24 '13 at 5:28

I tried timing a similar example on my machine, and I found that the times were the same. Has anyone else tried timing it?
– gsingh2011May 30 '13 at 0:41

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@Gauthier: yes, the first snippet is the good one; I think that when I wrote this I was thinking along the lines of "All it takes [to ruin the performance of a working application] is to go from... to..."
– Matteo ItaliaDec 22 '16 at 10:20

Locality of Reference

The first factor (to which others have already alluded) is locality of reference. Locality of reference really has two dimensions though: space and time.

Spatial

The spatial dimension also comes down to two things: first, we want to pack our information densely, so more information will fit in that limited memory. This means (for example) that you need a major improvement in computational complexity to justify data structures based on small nodes joined by pointers.

Second, we want information that will be processed together also located together. A typical cache works in "lines", which means when you access some information, other information at nearby addresses will be loaded into the cache with the part we touched. For example, when I touch one byte, the cache might load 128 or 256 bytes near that one. To take advantage of that, you generally want the data arranged to maximize the likelihood that you'll also use that other data that was loaded at the same time.

For just a really trivial example, this can mean that a linear search can be much more competitive with a binary search than you'd expect. Once you've loaded one item from a cache line, using the rest of the data in that cache line is almost free. A binary search becomes noticeably faster only when the data is large enough that the binary search reduces the number of cache lines you access.

Time

The time dimension means that when you do some operations on some data, you want (as much as possible) to do all the operations on that data at once.

Since you've tagged this as C++, I'll point to a classic example of a relatively cache-unfriendly design: std::valarray. valarray overloads most arithmetic operators, so I can (for example) say a = b + c + d; (where a, b, c and d are all valarrays) to do element-wise addition of those arrays.

The problem with this is that it walks through one pair of inputs, puts results in a temporary, walks through another pair of inputs, and so on. With a lot of data, the result from one computation may disappear from the cache before it's used in the next computation, so we end up reading (and writing) the data repeatedly before we get our final result. If each element of the final result will be something like (a[n] + b[n]) * (c[n] + d[n]);, we'd generally prefer to read each a[n], b[n], c[n] and d[n] once, do the computation, write the result, increment n and repeat 'til we're done.2

Line Sharing

The second major factor is avoiding line sharing. To understand this, we probably need to back up and look a little at how caches are organized. The simplest form of cache is direct mapped. This means one address in main memory can only be stored in one specific spot in the cache. If we're using two data items that map to the same spot in the cache, it works badly -- each time we use one data item, the other has to be flushed from the cache to make room for the other. The rest of the cache might be empty, but those items won't use other parts of the cache.

To prevent this, most caches are what are called "set associative". For example, in a 4-way set-associative cache, any item from main memory can be stored at any of 4 different places in the cache. So, when the cache is going to load an item, it looks for the least recently used3 item among those four, flushes it to main memory, and loads the new item in its place.

The problem is probably fairly obvious: for a direct-mapped cache, two operands that happen to map to the same cache location can lead to bad behavior. An N-way set-associative cache increases the number from 2 to N+1. Organizing a cache into more "ways" takes extra circuitry and generally runs slower, so (for example) an 8192-way set associative cache is rarely a good solution either.

Ultimately, this factor is more difficult to control in portable code though. Your control over where your data is placed is usually fairly limited. Worse, the exact mapping from address to cache varies between otherwise similar processors. In some cases, however, it can be worth doing things like allocating a large buffer, and then using only parts of what you allocated to ensure against data sharing the same cache lines (even though you'll probably need to detect the exact processor and act accordingly to do this).

False Sharing

There's another, related item called "false sharing". This arises in a multiprocessor or multicore system, where two (or more) processors/cores have data that's separate, but falls in the same cache line. This forces the two processors/cores to coordinate their access to the data, even though each has its own, separate data item. Especially if the two modify the data in alternation, this can lead to a massive slowdown as the data has to be constantly shuttled between the processors. This can't easily be cured by organizing the cache into more "ways" or anything like that either. The primary way to prevent it is to ensure that two threads rarely (preferably never) modify data that could possibly be in the same cache line (with the same caveats about difficulty of controlling the addresses at which data is allocated).

Those who know C++ well might wonder if this is open to optimization via something like expression templates. I'm pretty sure the answer is that yes, it could be done and if it was, it would probably be a pretty substantial win. I'm not aware of anybody having done so, however, and given how little valarray gets used, I'd be at least a little surprised to see anybody do so either.

In case anybody wonders how valarray (designed specifically for performance) could be this badly wrong, it comes down to one thing: it was really designed for machines like the older Crays, that used fast main memory and no cache. For them, this really was a nearly ideal design.

Yes, I'm simplifying: most caches don't really measure the least recently used item precisely, but they use some heuristic that's intended to be close to that without having to keep a full time-stamp for each access.

If the cache line size is 64 bytes, and we are operating on 32 bit (4 byte) floats, then there are 16 items per cache line. And the number of cache misses via just this simple transformation is reduced approximately 16-fold.

People who read this might also be interested in my article about matrix multiplication where I tested the "cache-friendly" ikj-algorithm and the unfriendly ijk-algorithm by multiplying two 2000x2000 matrices.
– Martin ThomaMay 29 '13 at 5:08

Processors today work with many levels of cascading memory areas. So the CPU will have a bunch of memory that is on the CPU chip itself. It has very fast access to this memory. There are different levels of cache each one slower access ( and larger ) than the next, until you get to system memory which is not on the CPU and is relatively much slower to access.

Logically, to the CPU's instruction set you just refer to memory addresses in a giant virtual address space. When you access a single memory address the CPU will go fetch it. in the old days it would fetch just that single address. But today the CPU will fetch a bunch of memory around the bit you asked for, and copy it into the cache. It assumes that if you asked for a particular address that is is highly likely that you are going to ask for an address nearby very soon. For example if you were copying a buffer you would read and write from consecutive addresses - one right after the other.

So today when you fetch an address it checks the first level of cache to see if it already read that address into cache, if it doesn't find it, then this is a cache miss and it has to go out to the next level of cache to find it, until it eventually has to go out into main memory.

Cache friendly code tries to keep accesses close together in memory so that you minimize cache misses.

So an example would be imagine you wanted to copy a giant 2 dimensional table. It is organized with reach row in consecutive in memory, and one row follow the next right after.

If you copied the elements one row at a time from left to right - that would be cache friendly. If you decided to copy the table one column at a time, you would copy the exact same amount of memory - but it would be cache unfriendly.

It needs to be clarified that not only data should be cache-friendly, it is just as important for the code. This is in addition to branch predicition, instruction reordering, avoiding actual divisions and other techniques.

Typically the denser the code, the fewer cache lines will be required to store it. This results in more cache lines being available for data.

The code should not call functions all over the place as they typically will require one or more cache lines of their own, resulting in fewer cache lines for data.

A function should begin at a cache line-alignment-friendly address. Though there are (gcc) compiler switches for this be aware that if the the functions are very short it might be wasteful for each one to occupy an entire cache line. For example, if three of the most often used functions fit inside one 64 byte cache line, this is less wasteful than if each one has its own line and results in two cache lines less available for other usage. A typical alignment value could be 32 or 16.

So spend some extra time to make the code dense. Test different constructs, compile and review the generated code size and profile.

As @Marc Claesen mentioned that one of the ways to write cache friendly code is to exploit the structure in which our data is stored. In addition to that another way to write cache friendly code is: change the way our data is stored; then write new code to access the data stored in this new structure.

This makes sense in the case of how database systems linearize the tuples of a table and store them. There are two basic ways to store the tuples of a table i.e. row store and column store. In row store as the name suggests the tuples are stored row wise. Lets suppose a table named Product being stored has 3 attributes i.e. int32_t key, char name[56] and int32_t price, so the total size of a tuple is 64 bytes.

We can simulate a very basic row store query execution in main memory by creating an array of Product structs with size N, where N is the number of rows in table. Such memory layout is also called array of structs. So the struct for Product can be like:

Similarly we can simulate a very basic column store query execution in main memory by creating an 3 arrays of size N, one array for each attribute of the Product table. Such memory layout is also called struct of arrays. So the 3 arrays for each attribute of Product can be like:

/* create separate arrays for each attribute */
int32_t* key = new int32_t[N];
char* name = new char[56*N];
int32_t* price = new int32_t[N];
/* now load these arrays, from a file etc. */

Now after loading both the array of structs (Row Layout) and the 3 separate arrays (Column Layout), we have row store and column store on our table Product present in our memory.

Now we move on to the cache friendly code part. Suppose that the workload on our table is such that we have an aggregation query on the price attribute. Such as

SELECT SUM(price)
FROM PRODUCT

For the row store we can convert the above SQL query into

int sum = 0;
for (int i=0; i<N; i++)
sum = sum + table[i].price;

For the column store we can convert the above SQL query into

int sum = 0;
for (int i=0; i<N; i++)
sum = sum + price[i];

The code for the column store would be faster than the code for the row layout in this query as it requires only a subset of attributes and in column layout we are doing just that i.e. only accessing the price column.

Suppose that the cache line size is 64 bytes.

In the case of row layout when a cache line is read, the price value of only 1(cacheline_size/product_struct_size = 64/64 = 1) tuple is read, because our struct size of 64 bytes and it fills our whole cache line, so for every tuple a cache miss occurs in case of a row layout.

In the case of column layout when a cache line is read, the price value of 16(cacheline_size/price_int_size = 64/4 = 16) tuples is read, because 16 contiguous price values stored in memory are brought into the cache, so for every sixteenth tuple a cache miss ocurs in case of column layout.

So the column layout will be faster in the case of given query, and is faster in such aggregation queries on a subset of columns of the table. You can try out such experiment for yourself using the data from TPC-H benchmark, and compare the run times for both the layouts. The wikipedia article on column oriented database systems is also good.

So in database systems, if the query workload is known beforehand, we can store our data in layouts which will suit the queries in workload and access data from these layouts. In the case of above example we created a column layout and changed our code to compute sum so that it became cache friendly.

Be aware that caches do not just cache continuous memory. They have multiple lines (at least 4) so discontinous and overlapping memory can often be stored just as efficiently.

What is missing from all the above examples is measured benchmarks. There are many myths about performance. Unless you measure it you do not know. Do not complicate your code unless you have a measured improvement.